J. Diaz and M. J. Grote, Energy Conserving Explicit Local Time Stepping for Second-Order Wave Equations, SIAM Journal on Scientific Computing, vol.31, issue.3, pp.1985-2014, 2009.
DOI : 10.1137/070709414
URL : https://hal.archives-ouvertes.fr/inria-00193160

F. Müller and C. Schwab, Finite Elements with mesh refinement for wave equations in polygons, Journal of Computational and Applied Mathematics, vol.283, 2013.
DOI : 10.1016/j.cam.2015.01.002

S. Osher and R. Sanders, Numerical approximations to nonlinear conservation laws with locally varying time and space grids, Mathematics of Computation, vol.41, issue.164, pp.321-336, 1983.
DOI : 10.1090/S0025-5718-1983-0717689-8

U. M. Ascher, S. J. Ruuth, and B. T. Wetton, Implicit-Explicit Methods for Time-Dependent Partial Differential Equations, SIAM Journal on Numerical Analysis, vol.32, issue.3, pp.797-823, 1995.
DOI : 10.1137/0732037

A. Kanevsky, M. H. Carpenter, D. Gottlieb, and J. S. Hesthaven, Application of implicit???explicit high order Runge???Kutta methods to discontinuous-Galerkin schemes, Journal of Computational Physics, vol.225, issue.2, pp.1753-1781, 2007.
DOI : 10.1016/j.jcp.2007.02.021

V. Dolean, H. Fahs, L. Fezoui, and S. Lanteri, Locally implicit discontinuous Galerkin method for time domain electromagnetics, Journal of Computational Physics, vol.229, issue.2, pp.512-526, 2010.
DOI : 10.1016/j.jcp.2009.09.038
URL : https://hal.archives-ouvertes.fr/inria-00403741

S. Descombes, S. Lanteri, and L. Moya, Locally Implicit Time Integration Strategies in a Discontinuous Galerkin Method for Maxwell???s Equations, Journal of Scientific Computing, vol.14, issue.3, pp.190-218, 2013.
DOI : 10.1109/TAP.1966.1138693

J. Verwer, Component splitting for semi-discrete Maxwell equations, BIT Numerical Mathematics, vol.14, issue.2, pp.427-445, 2011.
DOI : 10.1109/TAP.1966.1138693
URL : https://ir.cwi.nl/pub/18932/18932D.pdf

C. W. Gear and D. R. Wells, Multirate linear multistep methods, BIT, vol.39, issue.159, pp.484-502, 1984.
DOI : 10.1007/BF01934907

M. J. Grote and T. Mitkova, High-order explicit local time-stepping methods for damped wave equations, Journal of Computational and Applied Mathematics, vol.239, pp.270-289, 2013.
DOI : 10.1016/j.cam.2012.09.046
URL : https://doi.org/10.1016/j.cam.2012.09.046

M. Hochbruck and A. Ostermann, Exponential multistep methods of Adams-type, BIT Numerical Mathematics, vol.27, issue.2, pp.889-908, 2011.
DOI : 10.1007/BF01396634

M. J. Grote, M. Mehlin, and T. Mitkova, Runge-Kutta based explicit local time-stepping, Tech. rep, 2014.
DOI : 10.1137/140958293

F. Collino, T. Fouquet, and P. Joly, A conservative space-time mesh refinement method for the 1-D wave equation. I. Construction, Numer. Math, vol.95, issue.2, pp.197-221, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00989055

F. Collino, T. Fouquet, and P. Joly, A conservative space-time mesh refinement method for the 1-D wave equation, II. Analysis, Numer. Math, vol.95, issue.2, pp.223-251, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00989055

P. Joly and J. Rodríguez, An Error Analysis of Conservative Space-Time Mesh Refinement Methods for the One-Dimensional Wave Equation, SIAM Journal on Numerical Analysis, vol.43, issue.2, pp.825-859, 2005.
DOI : 10.1137/040603437

E. Bécache, P. Joly, and J. Rodríguez, Space???time mesh refinement for elastodynamics. Numerical results, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.2-5, pp.2-5, 2005.
DOI : 10.1016/j.cma.2004.02.023

F. Collino, T. Fouquet, and P. Joly, Conservative space-time mesh refinement methods for the FDTD solution of Maxwell???s equations, Journal of Computational Physics, vol.211, issue.1, pp.9-35, 2006.
DOI : 10.1016/j.jcp.2005.03.035

S. Piperno, Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems, ESAIM: Mathematical Modelling and Numerical Analysis, vol.16, issue.5, pp.815-841, 2006.
DOI : 10.1006/jcph.1996.0100
URL : https://hal.archives-ouvertes.fr/hal-00607709

M. J. Grote and T. Mitkova, Explicit local time-stepping methods for Maxwell???s equations, Journal of Computational and Applied Mathematics, vol.234, issue.12, pp.3283-3302, 2010.
DOI : 10.1016/j.cam.2010.04.028
URL : https://doi.org/10.1016/j.cam.2010.04.028

C. Baldassari, H. Barucq, H. Calandra, and J. Diaz, Numerical performances of a hybrid local-time stepping strategy applied to the reverse time migration, Geophysical Prospecting, vol.25, issue.5-40, pp.907-919, 2011.
DOI : 10.1090/S0025-5718-1971-0303766-4
URL : https://hal.archives-ouvertes.fr/hal-00627603

S. Minisini, E. Zhebel, A. Kononov, and W. A. Mulder, Local time stepping with the discontinuous Galerkin method for wave propagation in 3D heterogeneous media, GEOPHYSICS, vol.88, issue.3, pp.67-77, 2013.
DOI : 10.1007/s10444-004-7626-z

G. C. Cohen, Higher-Order Numerical Methods for Transient Wave Equations. Scientific Computation, Applied Mechanics Reviews, vol.55, issue.5, 2002.
DOI : 10.1115/1.1497470
URL : https://hal.archives-ouvertes.fr/hal-01166961

G. C. Cohen, P. Joly, J. E. Roberts, and N. Tordjman, Higher Order Triangular Finite Elements with Mass Lumping for the Wave Equation, SIAM Journal on Numerical Analysis, vol.38, issue.6, pp.38-2047, 2001.
DOI : 10.1137/S0036142997329554
URL : https://hal.archives-ouvertes.fr/hal-01010373

W. A. Mulder, HIGHER-ORDER MASS-LUMPED FINITE ELEMENTS FOR THE WAVE EQUATION, Journal of Computational Acoustics, vol.09, issue.02, pp.9-671, 2001.
DOI : 10.1190/1.1442241

G. A. Baker and V. A. Dougalis, The Effect of Quadrature Errors on Finite Element Approximations for Second Order Hyperbolic Equations, SIAM Journal on Numerical Analysis, vol.13, issue.4, pp.577-598, 1976.
DOI : 10.1137/0713049

C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods: Fundamentals in Single Domains, 2006.

M. J. Grote, A. Schneebeli, and D. Schötzau, Discontinuous Galerkin Finite Element Method for the Wave Equation, SIAM Journal on Numerical Analysis, vol.44, issue.6, pp.2408-2431, 2006.
DOI : 10.1137/05063194X
URL : https://hal.archives-ouvertes.fr/hal-01443184

M. A. Dablain, High order di?erencing for the scalar wave equation, SEG Technical Program Expanded Abstracts, 1984.

G. R. Shubin and J. B. Bell, A Modified Equation Approach to Constructing Fourth Order Methods for Acoustic Wave Propagation, SIAM Journal on Scientific and Statistical Computing, vol.8, issue.2, pp.135-151, 1987.
DOI : 10.1137/0908026

J. Gilbert and P. Joly, Higher Order Time Stepping for Second Order Hyperbolic Problems and Optimal CFL Conditions, pp.67-93, 2008.
DOI : 10.1007/978-1-4020-8758-5_4
URL : https://hal.archives-ouvertes.fr/hal-00976773

J. R. Shewchuk, Triangle: Engineering a 2d quality mesh generator and delaunay triangulator, in: Applied computational geometry towards geometric engineering, pp.203-222, 1996.

A. Henderson, The ParaView Guide, A Parallel Visualization Application, 2007.

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